Question 834377
Let {{{ a }}} = Joe's age now
Let {{{ b }}} = Jill's age now
{{{ a - 3 }}} = Joe's age 3 yrs ago
{{{ b - 3 }}} = Jill's age 3 yrs ago
{{{ a + 6 }}} = Joe's age in 6 yrs
{{{ b + 6 }}} = Jill's age in 6 yrs
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(1) {{{ a - 3 = 2*( b - 3 ) + 1 }}}
(2) {{{ a + 6  = (1/2)*( b + 6 ) + 10 }}}
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(1) {{{ a - 3 = 2b - 6 + 1 }}}
(1) {{{ a - 2b = -2 }}}
(1) {{{ -a + 2b = 2 }}}
and
(2) {{{ 2a + 12 = b + 6 + 20 }}}
(2) {{{ 2a - b = 14 }}}
Multiply both sides of (1) by {{{2}}}
and add (1) and (2)
(2) {{{ 2a - b = 14 }}}
(1) {{{ -2a + 4b = 4 }}}
{{{ 3b = 18 }}}
{{{ b = 6 }}}
and
(1) {{{ a - 2b = -2 }}}
(1) {{{ a = 2b - 2 }}}
(1) {{{ a = 12 - 2 }}}
(1) {{{ a = 10 }}}
Joe is 10 now
check:
Six yrs from now, Joe will be 16
Jill will be 12
Half her age is 6
Joe will be 1/2 of 6 + 10 = 16
OK